\(GL(m,2)\) acting on \(R(r,m)/R(r-1,m)\)

DOI10.1016/0012-365X(94)00342-GzbMath0852.94020MaRDI QIDQ1910572

Xiang-Dong Hou

Publication date: 25 March 1996

Published in: Discrete Mathematics (Search for Journal in Brave)

zbMATH Keywords

coveringautomorphism grouporbit sizesweight distributionsrepresentativesgeneral affine group

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Linear algebraic groups over finite fields (20G40) Linear codes (general theory) (94B05)

Related Items (18)

Analysis of affinely equivalent Boolean functions ⋮ On affine (non)equivalence of Boolean functions ⋮ Unnamed Item ⋮ Probabilistic estimation of the algebraic degree of Boolean functions ⋮ Unnamed Item ⋮ Counting all bent functions in dimension eight 99270589265934370305785861242880 ⋮ Counting Boolean functions with faster points ⋮ Some algebraic questions about the Reed-Muller code ⋮ On the number of the rational zeros of linearized polynomials and the second-order nonlinearity of cubic Boolean functions ⋮ Exact 2-divisibility of exponential sums associated to Boolean functions ⋮ Enumeration of isomorphism classes of extensions of \(p\)-adic fields. ⋮ The number of affine equivalent classes and extended affine equivalent classes of vectorial Boolean functions ⋮ New bounds on the covering radius of the second order Reed-Muller code of length 128 ⋮ Affinity of permutations of \(\mathbb F_{2}^{n}\) ⋮ Automorphism groups of Alexander quandles. ⋮ Classification of self dual quadratic bent functions ⋮ The covering radius of the Reed-Muller code \(\text{RM}(2, 7)\) is \(40\) ⋮ Cubic bent functions

Cites Work

• On ``bent functions
• Classification of cosets of the Reed-Muller code \(R(m-3,m)\)
• Further results on the covering radii of the Reed-Muller codes
• The Covering Radius of the $(m - 3)$rd Order Reed Muller Codes and a Lower Bound on the $(m - 4)$th Order Reed Muller Codes
• The Characters of the Finite General Linear Groups
• Covering radius---Survey and recent results
• The covering radius of the (128,8) Reed-Muller code is 56 (Corresp.)
• The second order Reed-Muller code of length 64 has covering radius 18 (Corresp.)
• On the Applications of Mobius Inversion in Combinatorial Analysis
• Some results on the covering radii of Reed-Muller codes
• Weight enumerator for second-order Reed-Muller codes
• Weight distributions of the cosets of the (32,6) Reed-Muller code
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